bee flies at 2020 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 1818? minutes, and then flies directly back to the hive at 1212 feet per second. It is away from the hive for a total of 2020 minutes. A. What equation can you use to find the distance of the flowerbed from the? hive? B. How far is the flowerbed from the? hive?

The equation we can use to find the distance is 20 x = 12 * (120-x)

The distance between hive and flower bed is 900 feet.

Step-by-step explanation:

Bee flies at 20 feet per second directly to a flowerbed from its hive.

It means forward speed is 20 feet/sec

The bee stays at the flowerbed for 18 mins

Then flies directly back to the hive at 12 feet per second.

So backward speed is 12 feet/second

It is away from the hive fore 20 minutes total

so,

total time = forward time + backward time + stay time

The bee stays at the flower bed for 18 minutes,

20 = forward time+backward time+18

20-18 = forward time + backward time

2 mins = forward time + backward time

Convert mins into seconds ...

2*60 = forward time + backward time

120 seconds = forward time + backward time

Part A:

Lets assume that forward time = x.

Backward time = 120-x

We know that

distance = speed*time

d = forward speed*forward time

d = 20*x

d = backward speed * forward time

d = 12 * (120-x)

20 x = 12 * (120-x)

The equation we can use to find the distance is 20 x = 12 * (120-x)

Part B:

20 x = 12 (120-x)

20 x = 1440-12 x

Combine the like terms:

20 x+12 x = 1440

32 x = 1440

Divide both sides by 32

32 x/32 = 1440/32

x = 45

Now we can find distance

d = 20*45

d = 900

The distance between hive and flower bed is 900 feet.